She’s held private meetings with Black Lives Matter activists, she rails against “systemic racism” and “white privilege,” and she’s made police brutality a focus of her campaign — but Hillary Clinton can’t seem to win the votes of the BLM movement.

The latest sign of discontent came Wednesday, when two BLM activists crashed a private fundraiser, demanding Mrs. Clinton apologize for comments she made 20 years ago as first lady, backing then-President Clinton’s get-tough crime legislation.

“You owe black people an apology,” Ashley Williams, a BLM protester, told Mrs. Clinton, holding a sign with bold, black letters of Mrs. Clinton’s past words: “We have to bring them to heel.”

Ms. Williams was escorted out of the event, but the bad blood between her movement and Mrs. Clinton is not so quickly dismissed, as the Democratic presidential campaign turns to South Carolina, which votes this Saturday, with an electorate where more than half of voters will be black.

Both Mrs. Clinton and her rival, Vermont Senator Bernard Sanders, are having a difficult time winning over BLM activists, despite their recent pledges to the African-American community.

Over the summer Mr. Sanders was forced off a stage in Seattle by BLM activists who were frustrated his focus on economic issues ignored many of their concerns about institutional racism in America.

Likewise, Mrs. Clinton was condemned by one activist after holding a closed-door meeting with the group in October for “victim blaming” after she recommended the group suggest specific policy changes rather than focusing on trying to convince white people of the impact racism has on black lives.

“Look, I don’t believe you change hearts. I believe you change laws, you change allocation of resources, you change the way systems operate. You’re not going to change every heart. You’re not. But, at the end of the day, we can do a whole lot to change some hearts and change some systems and create more opportunities for people who deserve to have them,” Mrs. Clinton told members of the group in a released video.

Tia Oso, an organizer for the Black Alliance for Just Immigration and a BLM activist who confronted Mr. Sanders in Seattle, was and still is not happy with that explanation.

“I felt like her comments then and her comments last night were very condescending. She’s been touting her record and readiness to lead the nation, yet is looking to us to submit policy proposals,” Ms. Oso said. “Doesn’t that seem imbalanced? I’ve never been a senator, I’ve never been secretary of state, I wasn’t the one advocating for these proposals as first lady. I’m a community member and grass-roots organizer who is suffering. She’s the policy expert that needs to address the issue.”

Both Mrs. Clinton and Mr. Sanders have stepped up their efforts to woo black voters, sharpening their criticism of racism and promising criminal justice reform.

Mrs. Clinton has touted the backing of the Congressional Black Caucus; of Rep. James E. Clyburn, the most senior black member of the House; and of the mothers of Trayvon Martin and Eric Garner, whose deaths gave rise to the BLM movement.

And on Tuesday Mrs. Clinton tweeted: “Recognizing privilege and dismantling systemic racism is on all of us.”

Mr. Sanders sharpened his tone as well, saying he would drastically reduce incarceration rates in his first term as president. He said it was “beyond unspeakable” that black men are disproportionately represented in the prison population.

Countering Mrs. Clinton’s plethora of endorsements, Mr. Sanders has rapper and activist Killer Mike stumping, and has movie director Spike Lee, who, in a radio advertisement running in South Carolina, calls on voters to “wake up” — a nod to his own civil rights film “Do the Right Thing.”

But analysts said the pivot seems disingenuous to black voters, coming only after the candidates spent their time in Iowa, New Hampshire and Nevada talking about other issues.

“There is the overall perception that Hillary Clinton is pandering, and it’s not a good place to start,” said Charles A. Gallagher, a professor of sociology at LaSalle University in Philadelphia. “I believe she does believe what she’s saying, but she waited until she had to say it because she had to win over other groups, like the middle-class educated man. She had to make sure she had a lock on people like me before she could move to the next constituency.

“So how do you demonstrate you’re genuine and are authentic on these [BLM] issues when you’ve ignored them for many months?” Mr. Gallagher said. “You’re now finally turning to them, and they realize this. Historically, the black and brown community is often ignored until a race is so close [that] they’re needed.”

Her history on criminal justice also leaves her open to attack — particularly backing her husband’s decision to sign the 1994 crime bill. Mr. Clinton last summer admitted that law lengthened prison sentences.

“She wants us to trust in her to address these issues, but she doesn’t want us to bring up that she’s responsible for advocating many of them. It’s not fair and is dishonest, and is eroding trust in certain sectors of the black community,” Ms. Oso said.